I think this one's hard, especially with older/larger birds. My husband did the slice-the-neck thing on our first drakes--they were like 12 weeks old, and it went fine. He tried it on an older drake a year or two later, and the drake wouldn't die. It kept writhing and it was traumatic. It took him 4 or more tries to end the duck. It was not very humane...and he's refused to harvest a duck since. I don't blame him.
I also was a neighbor's house, and they were trying to harvest their turkey. It did not go well. The turkey didn't die quickly and in the end they had to try to chop the head off while it was in the kill cone.
I think if you can love on that
chicken and give it a nice, swift end, it doesn't matter if it's the next slit or the head chop, as long as it's fast for the bird.